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arXiv · 2406.11379

On existence of Sadovskii vortex patch: A touching pair of symmetric counter-rotating uniform vortex

Kyudong Choi·In-Jee Jeong·Young-Jin Sim
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Abstract

The Sadovskii vortex patch is a traveling wave for the two-dimensional incompressible Euler equations consisting of an odd symmetric pair of vortex patches touching the symmetry axis. Its existence was first suggested by numerical computations of Sadovskii in [J. Appl. Math. Mech., 1971], and has gained significant interest due to its relevance in inviscid limit of planar flows via Prandtl--Batchelor theory and as the asymptotic state for vortex ring dynamics. In this work, we prove the existence of a Sadovskii vortex patch, by solving the energy maximization problem under the exact impulse condition and an upper bound on the circulation.

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Kyudong Choi, In-Jee Jeong, Young-Jin Sim. 2024-06-17. On existence of Sadovskii vortex patch: A touching pair of symmetric counter-rotating uniform vortex. https://arxiv.org/abs/2406.11379

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